A. N. Prior’s System Q: A Review

Farshad Badie

Аннотация


In his “Time and Modality”, based on his own philosophical motivations, Arthur Norman Prior proposed the modal logic Q as a correct modal logic in 1957. Prior developed Q in order to offer a logic for contingent beings, in which one could rationally state that some beings are contingent and some are necessary. One may say that Q is an actualist modal logic with a natural semantics. This review article is a developed description/discussion of/on “The System Q” that is the fifth chapter of “Time and Modality”. I have attempted to analyse the logical structure of system Q in order to provide a more understandable description as well as logical analysis for today’s logicians, philosophers, and information-computer scientists. In the paper, the Polish notations are translated into modern notations in order to be more comprehensible and to support the developed formal descriptions and semantic analysis.

Полный текст:

PDF

Литература


Akama, Nagata 2005 — Akama S., Nagata Y. On Prior’s three-valued modal logic Q // The 35th International Symposium on Multiple-Valued Logic (ISMVL’05). Calgary, BC, 2005. P. 14–19.

Ballarin 2017 — Ballarin R. Modern Origins of Modal Logic // The Stanford Encyclopedia of Philosophy / ed. by E. N. Zalta. 2017. URL: https://plato.stanford.edu/archives/ sum2017/entries/logic-modal-origins/ (accessed: 29.11.2021).

Bull 1964 — Bull R. A. An Axiomatisation of Prior’s Modal Calculus Q // Notre Dame Journal of Formal Logic. 1964. Vol. 5, no. 3. P. 211–214. DOi: 10.1305/ndjfl/1093957880 .

Chellas 1980 — Chellas B. F. Modal Logic: An Introduction. Cambridge University Press, 1980.

Halldén 1951 — Halldén S. On the Semantic Non-completeness of Certain Lewis Calculi // Journal of Symbolic Logic. 1951. Vol. XIV. P. 127–129.

Hasle et al. 2003 — Hasle P. S., Øhrstrøm P., Braüner T., Copeland J. (eds.). Tense-Logic for Non-Permanent Existents // Arthur N. Prior. Papers on Time and Tense. New Edition. Oxford University Press, 2003. P. 257–274.

Heyting 1930 — Heyting A. Die formalen Regeln der intuitionistischen Logik // Sitzungsbericht Preußische Akademie der Wissenschaften Berlin, physikalisch-mathematische Klasse II. 1930. S. 42-56; 57–71.

Hughes, Cresswell 1968 — Hughes G., Cresswell M. J. An Introduction to Modal Logic. London: Methuen, 1986.

Lemmon 1956 — Lemmon E. J. Alternative Postulate-sets for Lewis’s S5 // Journal of Symbolic Logic. 1956. Vol. 21, no. 4. P. 347–349.

Łukasiewicz 1953 — Łukasiewicz J. A system of modal logic // The Journal of Computing Systems. 1953. Vol. 1, no. 3. P. 111–149.

Prior 1957 — Prior A. N. Time and Modality. Oxford: Oxford University Press, 1957.

Prior 1959 — Prior A. N. Notes on a Group of New Modal Systems // Logique et Analyse. 1959. Vol. 2, no. 6–7. P. 122–127.

Prior 1964 — Prior A. N. Axiomatisations of the Modal Calculus Q // Notre Dame Journal of Formal Logic. 1964. Vol. 5, no. 3. P. 215–217.

Prior 1967 — Prior A. N. Past, Present and Future. Oxford: Clarendon Press, 1967.

Smiley 1961 — Smiley T. On Łukasiewicz’s Ł-modal system // Notre Dame Journal of Formal Logic. 1961. Vol. 2, no. 3. P. 149–153. DOi: 10.1305/ndjfl/1093956874.




DOI: https://doi.org/10.52119/LPHS.2021.61.96.001

Ссылки

  • На текущий момент ссылки отсутствуют.


Bookmark and Share


(c) 2021 Farshad Badie

Лицензия Creative Commons
Это произведение доступно по лицензии Creative Commons «Attribution-NonCommercial» («Атрибуция — Некоммерческое использование») 4.0 Всемирная.